Michael Sandel was only 21 when fate brought him into dramatically close contact with the big questions of morality that would come to dominate his life. In 1974, while at university, he landed a summer internship at the Houston Chronicle's understaffed Washington bureau, and ended up covering Watergate — sitting in on the Supreme Court deliberations on the Nixon tapes, and the subsequent impeachment hearings on Capitol Hill. "At the end of that summer, my boss, the bureau chief, was musing about what an incredible story it had been, and he said maybe he would retire now, because it would never be this exciting again," he recalls. "This was a man in his mid-50s. I remember saying to him: 'At least you've had a career already. I'm 21. What am I to think? Are you telling me it's all downhill from here?'" This may explain Sandel's decision to shift from the particularities of political journalism to the abstractions of political philosophy: the timeless dilemmas of right and wrong never lose their importance. His talent, as a philosopher, is to inject such debates with some of the adrenaline more usually associated with the world of news and scandal.

The course Sandel teaches at Harvard, called "Justice", regularly attracts 1,200 students, who crowd into the university's largest lecture theatre, while in Britain he is best known for delivering this year's BBC Reith lectures on morality and markets. Now he is attempting to bring ethics to a wider audience still, with a new book based on the Harvard course, and a series on American public television that can be viewed at www.justiceharvard.org. On stage, Sandel adopts an appealing diffidence, not foisting wisdom on his students so much as coaxing them to confront their own moral hunches, and the sometimes contradictory principles underlying them. Why does it feel wrong, to so many people, to pay for a surrogate pregnancy, even if everyone involved gives their free consent? Why do so many people who think abortion is murder believe that it's permissible in cases of rape? If talent is an accident of birth, why is it assumed to be fair for Tiger Woods or David Beckham to keep the millions they make from their skills? If you support voluntary euthanasia, what's your basis for assuming that each of us has the ultimate right to dispose of our own lives?

According to a well-worn urban legend, Sandel was the inspiration for the character of Montgomery Burns in The Simpsons — the heartless, cackling nuclear power plant owner who thinks nothing of bribing safety inspectors, or blocking out the sun so that his customers will be forced to use more electricity. There is a certain physical resemblance. (Several Simpsons writers took the Justice course as undergraduates, and presumably basing such an amoral villain on someone so concerned with morals was part of the joke.) But watching Sandel deliver a public lecture in a 4,000-seater open-air amphitheatre at the Chautauqua Institution, a religious studies centre in upstate New York modelled on ancient Greece, more flattering parallels spring to mind: he is Socrates, or maybe Aristotle. Sandel doesn't spurn the comparison. "Aristotle was on to this," he says, of his belief that his audience's moral intuitions are as important as any theory he might wish to impart. "He thought that ordinary opinion wasn't just something that stood in need of correction. It was the starting-point of philosophy."

When Sandel delivered his well-received Reiths, there was a slight sense that he was preaching to the converted, telling London's left-leaning elites what they wanted to hear. Markets, he argued, had colonised too much of society, spreading unchecked into healthcare, education and military matters with unforeseen moral consequences. It is a modern-day article of faith – shared by Blair and Clinton, as well as Thatcher and Reagan – that markets are essentially neutral, an efficient mechanism for distributing resources, whether as a means to rightwing or leftwing ends. Yet the truth, Sandel said, is that they subtly distort any sphere of life they enter, altering people's motivations and values. As an illustration, he told the story of an after-school centre that tried to eradicate the problem of parents turning up late for their children by levying a fine: after they did so, parental lateness actually increased, because parents came to see the fine as a fee they chose to pay in return for extra childcare. The same problem, Sandel suggested, applies to carbon emissions trading. Destroying the planet stops being a moral offence, and becomes a mere cost of doing business.

Yet the Reith lectures represented only a slice of Sandel's thinking. Explored further, his work leads to conclusions just as unsettling for left-liberal types as for market zealots. He has built his academic career on exposing hypocrisies and inconsistencies at both ends of the political spectrum, forging an alternative vision of politics that he calls civic republicanism, but which is usually filed, a little awkwardly, under "communitarianism". "I get into a lot of trouble with my liberal friends, and in liberal journals, for this sort of thing," he says. "They say, 'Oh, that sounds terribly conservative,' and so on. Well, part of it looks conservative, part of it looks leftwing. I say: so be it. Maybe our politics needs to be reorganised."

Sandel's new book, Justice: What's The Right Thing to Do?, attempts to show that most of our current notions of justice and fairness, whether leftwing or rightwing, share one problematic assumption: the idea that our political system should embody "a certain kind of neutrality". Fiscal conservatives think politicians have no business deciding how we spend our money, so they oppose high taxes; social liberals think politicians have no business deciding who we marry, so they support gay marriage. Advocates of big government want the state to create a level playing-field on which all can freely pursue their own plans, whatever they may be, while small-government proponents think such policies get in the way of such freedom. What they all share, Sandel argues, is a belief that it's possible to talk about a "fair" or "just" society without getting involved in questions of morality or virtue – remaining neutral on the question of what, exactly, it means to live a good life, or to be a good citizen. "Whether you're a libertarian liberal or a more egalitarian liberal," he says, "the idea is that justice means being non-judgmental with respect to the preferences people bring to public life." Politics, looked at this way, works like a market: it is a technical, fundamentally neutral mechanism for helping people with different ideas about "the good" to live peaceably together, without judging between those ideas.

This orthodoxy is so deeply embedded that it can be hard to see that it is only one way of thinking about politics, and Sandel's alternative perspective can take a while to sink in. Whenever we have political arguments, he insists, we are inevitably arguing about morals and the definition of a virtuous life, whether we admit it or not. Supporters of gay marriage don't really think the state has no business telling you who to marry: if they really believed that, they would argue that the state should have no role in marriage whatsoever. What they really believe – as Sandel does – is that gay marriage is actively good, and worthy of being endorsed by the state. Likewise, to be pro-choice isn't really to remain neutral on the question of whether abortion is murder: rather, it is to declare that it is not. "To argue about justice," Sandel says, "is unavoidably to argue about virtues, about substantive moral and even spiritual questions."

The ancient Greeks and Romans, he notes, would never have stood for such an insipid notion as the neutral political sphere, with politicians and institutions acting like little more than football referees. Politics, Aristotle thought, was the highest and best way to spend one's life — a transformative experience in which one grappled with the biggest questions of existence. Our current politics, by contrast, seems to require citizens "to leave their deepest moral convictions at the door when they enter". Perhaps it's little wonder that so many are so cynical about public life, or that MPs feel justified in fiddling their expenses: our political philosophies themselves may have sapped politics of its moral weight. In Sandel's view, Barack Obama won last year's US presidential election because he understood that there was a widespread yearning for civic life to mean more. On the campaign trail, his language, as Sandel noted in the Reiths, "was very alive to the hunger for a politics of moral and spiritual resonance".

Sandel's preoccupation with politics can be traced back at least as far as his days as a high-school student – and, specifically, to an incident involving Ronald Reagan and some jellybeans. Born in Minneapolis in 1953, the son of a record salesman, Sandel moved to California as a child and attended a school in Pacific Palisades, near the home of Reagan, then state governor. "I was the student body president," Sandel says, "and thought it would be interesting if I could persuade him to come to speak to the student body" – an almost uniformly long-haired, leftwing group who disagreed with Reagan on everything. A letter to the governor's office went unanswered. "But then my mother read, in a magazine article, that he loved jellybeans. So I got a six-pound bag of jellybeans, put them in a box with a ribbon and an invitation, and took them to his house." The state troopers guarding Reagan from Vietnam protesters were suspicious, but let the jellybeans through. "A few days later he called the school, and said he'd come."

Sandel, who was to interview Reagan, had prepared "a list of very, very tough questions I was sure I could grill him on – such as why was he against the 18-year-old vote when he believed 18-year-olds could be drafted to fight in Vietnam? But one by one, he answered them with great charm, and then we opened questions to the floor . . . He charmed everyone, and people clapped, and out he went, and I didn't lay a glove on him."

Sandel graduated from Brandeis university in 1975, then went to Oxford's Balliol College as a Rhodes scholar, where he worked under Charles Taylor, Alan Montefiore, Ronald Dworkin and others. He was still toying with a career in journalism or economics when, preparing to leave for Spain one summer, Montefiore suggested some challenging holiday reading: Kant's Critique of Pure Reason. "I became hooked, and never really emerged," Sandel says now. "Before I knew it, these other careers fell away, and I shifted to political philosophy." In 1980 he started teaching at Harvard, where he met his wife, the social scientist Kiku Adatto; they have two sons. "When I arrived at Harvard, I wanted to design a course in political theory that would have interested me, back when I was started out, in a way that the standard things didn't." The result was the justice course.

In the early 80s, political philosophy at Harvard was dominated by John Rawls, whose magnum opus, A Theory of Justice, had been credited with reviving the entire field. The book seeks to reconcile the principles of liberty and equality, advocating a more egalitarian society. Sandel sympathised with Rawls's focus on equality – an unfashionable furrow to plough in American political thought at the time – but had nonetheless built his PhD thesis on attacking Rawls's work, especially its notion of politics as a morally neutral zone. It was published in 1982 as Liberalism and the Limits of Justice, and it established Sandel's reputation.

The notion of politics as a moral enterprise tends to trouble liberals: they fear that it might result in what Alexis de Tocqueville termed "the tyranny of the majority", trampling on the rights of those who don't happen to share society's prevailing moral position on any given issue, and giving free reign to racism, nationalism and mob rule. Committed secularists object particularly strongly to Sandel's position that arguments originating from religious or spiritual conviction should be granted a special respect, not treated as mere preferences, like a love of football or ice-cream. To ask a deeply religious Christian to participate in politics while putting their Christianity aside, he argues, is really to ask them not to participate in politics, as themselves, at all.

Sandel maintains that he is no majoritarian: a more engaged citizenry, he argues, would actually provide a far stronger check on abuses of power, or on over-powerful religious organisations. According to this view, it's precisely when most people refuse to admit religion into the public realm that extremists emerge to fill the vacuum and feed the hunger. It is in "a public life that is so emptied of moral meaning and resonance," he says, "that the narrowest, most intolerant forms of moralism will enter, and try to dominate that space." It may be no coincidence that the rise of terrorism motivated by religious extremism has parallelled the spread of market society and morally neutral politics.

Yet one need not share Sandel's optimism about a more religious public life in order to empathise with his sense that our politics has become impoverished, and that we might aspire to remake it as something more meaningful, even noble. An anecdote from his Watergate days seems to crystallise this. Nixon's crimes, of course, played an important role in breeding cynicism about politicians – but what sticks in Sandel's mind is how seriously, and uncynically, the members of Congress who impeached him took their duties. Two decades later, Bill Clinton's impeachment trial would descend into purely partisan bickering. But after the House judiciary committee had voted to impeach Nixon, things felt very different when Sandel approached one of the committe members, the African-American congresswoman from Texas, Barbara Jordan, for a quote.

"Obviously, my paper had a special responsibility for Houston, so you go up to the hometown member and ask her to say something," he recalls. "I'd spoken to her throughout, so she knew who I was. She had enormous presence – she was a very personally powerful figure with a stentorian voice. I rushed up and asked her some completely innocuous question – 'How does it feel to be voting for the impeachment of the president?' or something like that, just to get a quote.

"She snapped at me. Her voice was breaking. She said: 'I don't feel like answering any questions from anybody at this moment.' And she went off with tears in her eyes. She had no sympathy for Nixon, of course. But she was so moved by the gravity of the situation – by the sense of constitutional moment – that she would not speak. I was shaking. It was an innocent time, compared to the politics we have now."